Hyperbolic Rules in Genomes, the Harmonic Progression and Recurrence Sequences in Algebraic Biology

Mapping Intimacies ◽

10.20944/preprints202008.0398.v1 ◽

2020 ◽

Author(s):

Sergey V. Petoukhov

Keyword(s):

Coding System ◽

Mathematical Objects ◽

Harmonic Progression ◽

Natural Logarithm ◽

Urgent Task ◽

Logarithmic Spirals ◽

Algebraic Biology ◽

Recurrence Sequences ◽

Cooperative Organization ◽

Scale Transformations

The article is devoted to biological models using recurrence sequences, which are connected with the harmonic progression 1, 1/2, …, 1/n, and some cooperative properties of genomes. The harmonic progression is itself one of the recurrence sequences based on the harmonic mean. This progression appears in the hyperbolic rules of oligomer cooperative organization in eukaryotic and prokaryotic genomes. This allows thinking that the harmonic progression is also related to inherited physiological systems, which must be structurally consistent with the genetic coding system for their transmission to descendants and survival in evolution. The harmonic progression is one of historically known mathematical series, whose features were studied by Pythagoras, Leibniz, Newton, Euler, Fourier, Dirichlet, Riemann. It is widely used in many known algorithms and is closely related to some other important mathematical objects, for example, the function of the natural logarithm and harmonic numbers. Accordingly, the article describes the possibilities of using these interrelated mathematical objects to model biological structures, including logarithmic spirals and some other. Modeling inherited spiral configurations seems to be a particularly urgent task, since they are extremely common at all levels of organization of living bodies and, according to Goethe, are lines of life. The principle of a recurrence similarity, that is a special similarity of parts and transformations presented in recurrence sequences of numbers and matrix operators (the scale similarity and scale transformations are only particular cases of such similarity), is considered as one of the key principles of structural organization of living bodies.

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Hyperbolic Rules of the Oligomer Cooperative Organization of Eukaryotic and Prokaryotic Genomes

10.20944/preprints202005.0471.v1 ◽

2020 ◽

Author(s):

Sergey Petoukhov

Keyword(s):

Quantum Information ◽

Dna Sequences ◽

Coding System ◽

Harmonic Progression ◽

General Rules ◽

Prokaryotic Genomes ◽

Algebraic Invariants ◽

Cooperative Organization ◽

Long Genes

The author's method of oligomer sums for analysis of oligomer compositions of eukaryotic and prokaryotic genomes is described. The use of this method revealed the existence of general rules for cooperative oligomeric organization of a wide list of genomes. These rules are called hyperbolic because they are associated with hyperbolic sequences including the harmonic progression 1, 1/2, 1/3, .., 1/n. These rules are demonstrated by examples of quantitative analysis of many genomes from the human genome to the genomes of archaea and bacteria. The hyperbolic (harmonic) rules, speaking about the existence of algebraic invariants in full genomic sequences, are considered as candidates for the role of universal rules for cooperative organization of genomes. The described phenomenological results were obtained as consequences of the previously published author's quantum-information model of long DNA sequences. The oligomer sums method was also applied to the analysis of long genes and viruses including the COVID-19 virus; this revealed, in characteristics of many of them, the phenomenon of rhythmically repeating deviations from model hyperbolic sequences; these deviations are associated with DNA triplets and should be systematically analyzed for a deeper understanding the genetic coding system. The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.

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Non-Euclidean Biosymmetries and Algebraic Harmony in Genomes of Higher and Lower Organisms

EPJ Web of Conferences ◽

10.1051/epjconf/202124801010 ◽

2021 ◽

Vol 248 ◽

pp. 01010

Author(s):

Sergey Petoukhov ◽

Elena Petukhova ◽

Vitaly Svirin

Keyword(s):

Projective Geometry ◽

Double Helix ◽

Nucleotide Sequences ◽

Cross Ratio ◽

Harmonic Progression ◽

The Cross ◽

Dna Double Helix ◽

Cooperative Organization ◽

Relationship Of ◽

The Relationship

The article is devoted to the study of the relationship of non-Euclidean symmetries in inherited biostructures with algebraic features of information nucleotide sequences in DNA molecules in the genomes of eukaryotes and prokaryotes. These genomic sequences obey the universal hyperbolic rules of the oligomer cooperative organization, which are associated with the harmonic progression 1/1, 1/2, 1/3,.., 1/n. The progression has long been known and studied in various branches of mathematics and physics. Now it has manifested itself in genetic informatics. The performed analysis of the harmonic progression revealed its connection with the cross-ratio, which is the main invariant of projective geometry. This connection consists in the fact that the magnitude of the cross-ratio is the same and is equal to 4/3 for any four adjacent members of this progression. The long DNA nucleotide sequences have fractal-like structure with so called epi-chains, whose structures are also related to the harmonic progression and the projective-geometrical symmetries. The received results are related additionally to a consideration of DNA double helix as helical antenna. This fact of the connection of genetic informatics with the main invariant of projective geometry can be used to explain the implementation of some non-Euclidean symmetries in genetically inherited structures of living bodies.

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Harmonic Progression in Bioinformatics and Recurrent Series in Inherited Biostructures

EPJ Web of Conferences ◽

10.1051/epjconf/202124801011 ◽

2021 ◽

Vol 248 ◽

pp. 01011

Author(s):

Vladimir Verevkin ◽

Sergey Petoukhov

Keyword(s):

Mathematical Models ◽

Biological Systems ◽

Molecular Genetic ◽

Standing Waves ◽

Genetic System ◽

Coding System ◽

Harmonic Progression ◽

Structural Relationships ◽

Logarithmic Law ◽

Long Range Communication

The article is devoted to the study of new approaches to the development of mathematical models in genetic biomechanics, which studies the structural relationships of the genetic coding system with genetically inherited biological forms. More specifically, we are talking about models based on the recurrent harmonic progression whose connection with the information sequences of DNA molecules in the genomes of higher and lower organisms was recently revealed. In particular, the article describes previously unknown connections of the function of natural logarithms with the structures of the molecular genetic system, which allow modelling the main psychophysical logarithmic law by Weber-Fechner and also many other logarithmic structures in genetically inherited biological systems. In physics, the harmonic progression is traditionally considered, first of all, as related to standing waves in resonators. Our results are correlated with Frohlich’s vibration-resonant theory about collective quantum effects and long-range communication in biological systems.

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Hyperbolic Rules of the Oligomer Cooperative Organization of Eukaryotic and Prokaryotic Genomes

10.20944/preprints202005.0471.v2 ◽

2020 ◽

Author(s):

Sergey Petoukhov

Keyword(s):

Quantum Information ◽

Dna Sequences ◽

Amino Acid Sequences ◽

Literary Texts ◽

Harmonic Progression ◽

General Rules ◽

Prokaryotic Genomes ◽

Cooperative Organization ◽

Long Genes

The author's method of oligomer sums for analysis of oligomer compositions of eukaryotic and prokaryotic genomes is described. The use of this method revealed the existence of general rules for cooperative oligomeric organization of a wide list of genomes. These rules are called hyperbolic because they are associated with hyperbolic sequences including the harmonic progression 1, 1/2, 1/3, .., 1/n. These rules are demonstrated by examples of quantitative analysis of many genomes from the human genome to the genomes of archaea and bacteria. The hyperbolic (harmonic) rules, speaking about the existence of algebraic invariants in full genomic sequences, are considered as candidates for the role of universal rules for the cooperative organization of genomes. The described phenomenological results were obtained as consequences of the previously published author's quantum-information model of long DNA sequences. The oligomer sums method was also applied to the analysis of long genes and viruses including the COVID-19 virus; this revealed, in characteristics of many of them, the phenomenon of such rhythmically repeating deviations from model hyperbolic sequences, which are associated with DNA triplets. In addition, an application of the oligomer sums method are shown to the analysis of the following long sequences: 1) amino acid sequences in long proteins like the protein Titin; 2) phonetic sequences of long Russan literary texts (for checking of thoughts of many authors that phonetic organization of human languages is deeply connected with the genetic language). The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.

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Application of Information Introduced to Dynamic Message Processing and Enjoyment

Journal of Media Psychology Theories Methods and Applications ◽

10.1027/1864-1105/a000195 ◽

2018 ◽

Vol 30 (4) ◽

pp. 196-206 ◽

Cited By ~ 4

Author(s):

Byungho Park ◽

Rachel L. Bailey

Keyword(s):

Resource Allocation ◽

Recognition Memory ◽

Emotional Processing ◽

Orienting Response ◽

Structural Features ◽

Cognitive Resources ◽

Coding System ◽

Message Complexity ◽

Cognitive Resource ◽

Cognitive Overload

Abstract. In an effort to quantify message complexity in such a way that predictions regarding the moment-to-moment cognitive and emotional processing of viewers would be made, Lang and her colleagues devised the coding system information introduced (or ii). This coding system quantifies the number of structural features that are known to consume cognitive resources and considers it in combination with the number of camera changes (cc) in the video, which supply additional cognitive resources owing to their elicitation of an orienting response. This study further validates ii using psychophysiological responses that index cognitive resource allocation and recognition memory. We also pose two novel hypotheses regarding the confluence of controlled and automatic processing and the effect of cognitive overload on enjoyment of messages. Thirty television advertisements were selected from a pool of 172 (all 20 s in length) based on their ii/cc ratio and ratings for their arousing content. Heart rate change over time showed significant deceleration (indicative of increased cognitive resource allocation) for messages with greater ii/cc ratios. Further, recognition memory worsened as ii/cc increased. It was also found that message complexity increases both automatic and controlled allocations to processing, and that the most complex messages may have created a state of cognitive overload, which was received as enjoyable by the participants in this television context.

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